Problem: Simplify the following expression: $\sqrt{24} + \sqrt{54}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{24} + \sqrt{54}$ $= \sqrt{4 \cdot 6} + \sqrt{9 \cdot 6}$ Separate the radicals and simplify. $= \sqrt{4} \cdot \sqrt{6} + \sqrt{9} \cdot \sqrt{6}$ $= 2\sqrt{6} + 3\sqrt{6}$ Finally, simplify by combining the terms. $= ( 2 + 3 )\sqrt{6} = 5\sqrt{6}$